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Existence theory for pseudo-symmetric solution to \(p\)-Laplacian differential equations involving derivative. (English) Zbl 1226.34017

The authors study the existence of one, three, or more positive pseudo-symmetric solutions for the boundary value problem
\[ \begin{gathered} (\varphi_{p}(u'(t)))'+h(t)f(t,u(t),u'(t))=0,\;t \in [0,1],\\ u(0) =0,\;u(1) =u(\eta),\;\eta \in (0,1),\end{gathered} \]
where \(\varphi_{p}\) is the \(p\)-Laplacian operator and \(h\) and \(f\) are pseudo-symmetric solutions about \(\eta\).
The authors use the classical theorem of cone compressions and expansions of Krasnosel’skii and the Avery-Peterson fixed point theorem.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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